What factors determine the coefficient of friction? I am doing a physics class online, and have a test next week and it is pretty hard to understand a physics class when you do not have the privilege of asking questions as often as i would like. So i am asking you to please help me better understand about friction.  


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*What factors determine the coefficient of friction? 

*What are some examples of materials with a low coefficient of friction and a high coefficient of friction? 
 A: Rest answers are fine. Just one more point that I would like to add to them is that smoothness doesn't always imply a low coefficient of friction. Since friction is not a fundamental force and it has electrostatic origins (read Feynman lectures on frictional forces), a highly smooth surface increase frictional forces between the objects as it brings atoms closer enough to interact with each other.
A: Tribology is a very complex scientific topic. There are different approaches how to describe the interaction between two sliding surfaces leading to different qualities to affect the Coefficient of Friction. Ones I can remember right now are:


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*The friction force is caused by asperity defformation
In this case the roughness and hardness are parameters influencing the CoF. The harder and smoother one surface is, the lower the CoF wil be. The rouher the harder surface is, the higher CoF and wear is.

*The friction force is caused by atomic forces between surfaces
In this case the smoother the surfaces are, the more bonds are formed between surfaces leading to higher CoF. The composition of the surfaces plays its role also, if the atoms in counterparts can form covalent bonds the CoF will be much higher than in case of materials forming Van der Vaals or hydrogen bonds.


There are also "other" phenomena to influence the CoF.


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*What is in between?
The surface to surface contact can be direct, theoretically, or there may be film of some fluid (lubricant or etchant), solid lubricant, dust or wear debris - material worn out from the counterparts. This can change the tribological properties of the contact completely.

*Temperature
Some surfaces change their behaviour with temerature more significantly tha the others, some may melt to form lubricating liquid film, some may weld together with the counterpart.

*Sliding speed
With higher speeds the asperities may have not enough time to lock as much as in case of slower speeds leading to lower volumes to be deformed leading to lower CoF. In case of lubricated contact the viscosity of the film may result in higher CoF for higer speeds.


And this is just a very brief and shallow insight.
A: Coefficient of friction is between two materials. So rubber would have a different coefficient of friction on pavement, than on glass. That said, some materials, like rubber, tend to have higher coefficients of friction with many other materials. Other materials, like PTFE and ice, have low coefficients of friction with many other materials. Ice is often given as an example of a material that has a low coefficient of friction. Below is a summary explanation of some of the effects that influence coefficient of friction. For more detail, this topic falls under the category of tribology.
Surface Roughness +
If two materials are both extremely rough (like <200 grit sandpaper) then the parts that stick up on one surface (asperities) will often find their way into the valleys of the other surface, like gear teeth. This interaction helps prevent the surfaces from sliding against each other. Thus, higher roughness materials will often have higher coefficients of friction.
Lubrication -
Often times there will be some media that is easily deformable that sits between the two surfaces. The oil in your engine separates the steel parts so well that the steel doesn't actually touch at all. In this case the friction force is actually due to the viscous effects of the oil deforming, and is highly velocity dependent. A wet road has a lower coefficient of friction with rubber than a dry road, due to the water acting as a lubricant. Ice will self lubricate by melting, providing a layer of water to separate the ice crystals from the other surface. Other solids, like graphite, will self lubricate by breaking off tiny bits of themselves that will then act as lubrication.
Intermolecular forces +
When molecules get very close together they tend to interact. Often they want to hold onto each other, through the Van der Waals force or otherwise. This tends to increase friction. PTFE (trandnamed Teflon) tends to have very low intermolecular forces and as a result it tends to have low friction.
Stiffness ?
There are a lot of "tends to" and "often"s in the above paragraphs due to how these (and other) effects interact. For example, increasing surface roughness can actually decrease friction if it allows for lubrication to better fill the gaps between the surfaces. It could also decrease friction by just separating most of the molecules from the other surface so the intermolecular forces are less. The stiffness of surfaces comes into play as one surface deforms another. For example rubber deforms very easily, which allows it to match the surface roughness of the other material, interlocking into it, and reducing the intermolecular distances to increase the intermolecular forces. This is one reason rubber tends to have high friction. Brass on the hand, while it also deforms easily, tends to deform in a way that rips off asperities, that then form lubricating particles. So brass's softness actually decreases friction.
A: A classic question, more difficult than it looks! I think the trick is to understand what doesn't determine the coefficient of friction.
(1) The weight of the object doesn't determine the coefficient of friction. You can see that it goes into the equation separately.
$$F_{\mu} = N\mu_k$$
where $F_{\mu}$ is the force of friction, N is the normal force (the weight), and $\mu_k$ is the coefficient of kinetic friction. 
(2) The size of the object doesn't determine the coefficient of friction! If I slide a cube along a table, and another cube of the same weight but twice the size, the force of friction doesn't change.
At this point you should conclude that no macroscopic properties of the object affect the coefficient of friction. It's entirely about the microscopic level picture.
So what does affect it? Intuitively, the "roughness" of the surface as mentioned in the comments. More generally, the answer is just "the two materials involved"
Here is a perfectly good list of some coefficients of friction. Note that each entry is for a combination of materials (for example: "wood on glass"), and it varies if they are dry or if there is something in-between the two materials (like water or a lubricant). There are some materials in the table that you don't encounter in everyday life, but I bet you can come up with some good examples just by thinking about what slides well across other things. For example, if you have a slanted, smooth table, would you put your metal phone on it without a case? What about with a rubber case?
A: Well the answer by Ravi is Right but I think it's a little over but in case if we're talking about Rolling friction coefficient then 
Coefficient of Friction actually depends on 3 things 


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*Directly Proportional to Normal 
 Reaction By Surface.

*Directly Proportional to Force of             Friction.  
3. Inversely proportional to   radius of rolling cylinder or wheel etc.
The Bold one shows the extra factor for rolling friction case, that's why I thought I should've answered tht.
